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Solving systems by graphing and tables : equations and inequalities

Solving systems by graphing and tables : equations and inequalities-example-1

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Given,

The system of inequalitites are,


\begin{gathered} 2x+3y>0 \\ x-y\leq5 \end{gathered}

The graph of the inequalities is,

The are three possible solution for the inequality.

For (0, 0),


\begin{gathered} 2x+3y>0 \\ 2(0)+3(0)>0 \\ 0>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 0-0\leq5 \\ 0\leq5 \end{gathered}

For (3, -2),


\begin{gathered} 2x+3y>0 \\ 2(3)+3(-2)>0 \\ 0>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 3-(-2)\leq5 \\ 5=5 \end{gathered}

For (5, 0),


\begin{gathered} 2x+3y>0 \\ 2(5)+3(0)>0 \\ 5>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 5-(0)\leq5 \\ 5=5 \end{gathered}

Hence, the solution of the inequalities is (5, 0).

Solving systems by graphing and tables : equations and inequalities-example-1
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